Physics of Difference IX: Collective Evaluation under Accessibility-Constrained Non-Factorizable Persistence

The present work investigates collective evaluation under accessibility-constrained non-factorizable latent distinction persistence. Previous PoD analyses established that distinct transformation pathways may remain compositionally distinguishable despite sharing identical reduced endpoint representation [5]. The present work investigates the structural consequences that arise once such latent distinctions remain globally persistent beyond local recoverability. The analysis begins from the observation that transformation distinction persistence may become distributed across focal structures, interacting structures, interaction consequences, and subsequent compositional organization. Under such conditions, globally persistent distinction structure no longer factorizes completely into independently reconstructible local sectors. The present framework therefore investigates situations in which: latent distinction persistence remains non-factorizable, only reduced sectors remain operationally accessible, and no accessibility-compatible reconstruction remains available. Under these conditions, independently recoverable transformation structure ceases to remain locally closed. Independently decomposed evaluation consequently becomes structurally incomplete. To investigate the resulting collectively dependent structure, the present work introduces a collectively dependent evaluation hierarchy: where independent evaluation appears as the lowest-order approximation and jointly dependent corrections emerge progressively at higher orders. Within this hierarchy, pairwise quadratic organization appears naturally as the leading nontrivial collectively dependent approximation, while higher-order jointly dependent structures remain structurally admissible whenever multiple transformation pathways remain jointly influential simultaneously. The resulting framework establishes the following structural progression: non-factorizable persistencerecoverability collapsecollective evaluationcollectively dependent hierarchy The present analysis further clarifies the structural relation between the current framework and existing approaches including decoherence, consistent histories, and generalized probabilistic frameworks. In particular, the present work investigates recoverability collapse prior to probabilistic assignment itself, thereby suggesting that probability-like collective organization may emerge from accessibility-constrained distributed latent distinction persistence rather than from primitive stochastic assumptions.